To do what?
I think the answer is simpler than that and two-fold. Mrs. Cruz is on an unpaid leave of absence from her job, where she had very good health insurance. She doesn't have that now, so Cruz has to get health care the same way the other Senators have to - either buy in privately and pay the whole cost or go through the D.C. healthcare exchange and get part of the cost paid for. That's the first part. The second is that getting rid of Obamacare is the centerpiece of his campaign. By having skin in the game then people can't accuse him of not caring about people having healthcare or not. He's out to end his own coverage along with everyone else's.
This is a simple issue. Ted Cruz respects the laws of this country, even those he vehemently disagrees with. He is following the statute because he is a law abiding citizen.